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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The simulation study presented in this research has two basic objectives. The first objective is to establish a consistency in the results for quantum transport in Silicon by comparing the results obtained by Anisur Rehman and M. Luisier, using the same transport method as used by them but in a slightly different device structure. Once the results are verified for Silicon, the second objective is to design a similar structure using GaAs in order to study the effects of GaAs on various transport parameters. The quantum transport model used in this research for MOSFET structures is the well-known Non Equilibrium Green s' Function (NEGF) formulation, which provides a powerful conceptual and computational framework for handling quantum transport in nano devices, and includes elastic scattering and strong correlation effects at atomic level. The comparative study of results obtained for Si and GaAs show that GaAs is not a better choice for ballistic transport due to low density of states inside the channel. Also the effect of exchange and correlation in GaAs device is negligible while the lower saturation voltage of Si allows it to be used for switching delays.